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The extra damage will not trigger if you are enchanted with Illusionary Weaponry as your attacks don't actually hit.
You can use an Icyupgrade for your martial weapons so that it will deal cold damage.
Even if you are wielding a weapon that deals cold damage the affects will not trigger if you are under the affects of skills that change damage type away from cold. Likewise if your weapon doesn't deal cold damage, you could use one of the skills that changed damage type to cold to achieve the desired affect. See Damage conversion skills for more references.